论文标题
分支过程中的祖传生殖偏见
Ancestral reproductive bias in branching processes
论文作者
论文摘要
考虑具有均匀繁殖法的分支过程。在一次$ t> 0 $的情况下，从人群中统一地对单个细胞进行采样，并沿着采样的细胞的祖先谱系看待，我们发现繁殖法是异质的 - 祖先细胞的预期生殖输出从时间上$ 0 $ $ 0 $ ty $ t $ t $ t $不断增加。这种“检查悖论”是由于抽样偏见引起的，具有较大后代的细胞更有可能将其后代之一取样，而这些后代的产物具有多种性，并且随机人口大小和/或抽样时间$ t $偏见的强度会增长。我们的主要结果明确表征了沿采样祖先谱系的繁殖速率和大小的演变，作为泊松过程的混合物，在特殊情况下简化了。祖先偏见有助于解释最近观察到的沿发展人类胚胎谱系的突变率的变化。
Consider a branching process with a homogeneous reproduction law. Sampling a single cell uniformly from the population at a time $T > 0$ and looking along the sampled cell's ancestral lineage, we find that the reproduction law is heterogeneous - the expected reproductive output of ancestral cells on the lineage from time $0$ to time $T$ continuously increases. This `inspection paradox' is due to sampling bias, that cells with a larger number of offspring are more likely to have one of their descendants sampled by virtue of their prolificity, and the bias's strength grows with the random population size and/or the sampling time $T$. Our main result explicitly characterises the evolution of reproduction rates and sizes along the sampled ancestral lineage as a mixture of Poisson processes, which simplifies in special cases. The ancestral bias helps to explain recently observed variation in mutation rates along lineages of the developing human embryo.
